#341682 (C++17) No.803 Very Limited Xor Subset

提出ソース
結果

問題	No.803 Very Limited Xor Subset
ユーザー	Pachicobue
提出日時	2019-04-23 19:20:36
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	28 ms / 2,000 ms
コード長	18,608 bytes
コンパイル時間	2,333 ms
コンパイル使用メモリ	211,456 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-10-15 13:40:15
合計ジャッジ時間	4,505 ms
ジャッジサーバーID （参考情報）	judge3 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	19 ms 5,248 KB
testcase_15	AC	20 ms 5,248 KB
testcase_16	AC	19 ms 5,248 KB
testcase_17	AC	20 ms 5,248 KB
testcase_18	AC	20 ms 5,248 KB
testcase_19	AC	20 ms 5,248 KB
testcase_20	AC	21 ms 5,248 KB
testcase_21	AC	20 ms 5,248 KB
testcase_22	AC	20 ms 5,248 KB
testcase_23	AC	28 ms 5,248 KB
testcase_24	AC	26 ms 5,248 KB
testcase_25	AC	27 ms 5,248 KB
testcase_26	AC	27 ms 5,248 KB
testcase_27	AC	26 ms 5,248 KB
testcase_28	AC	26 ms 5,248 KB
testcase_29	AC	26 ms 5,248 KB
testcase_30	AC	27 ms 5,248 KB
testcase_31	AC	27 ms 5,248 KB
testcase_32	AC	26 ms 5,248 KB
testcase_33	AC	26 ms 5,248 KB
testcase_34	AC	2 ms 5,248 KB
testcase_35	AC	24 ms 5,248 KB
testcase_36	AC	7 ms 5,248 KB
testcase_37	AC	12 ms 5,248 KB
testcase_38	AC	2 ms 5,248 KB
testcase_39	AC	2 ms 5,248 KB
testcase_40	AC	26 ms 5,248 KB
testcase_41	AC	25 ms 5,248 KB
testcase_42	AC	25 ms 5,248 KB
testcase_43	AC	26 ms 5,248 KB
testcase_44	AC	2 ms 5,248 KB
testcase_45	AC	2 ms 5,248 KB
testcase_46	AC	2 ms 5,248 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//!  dP     dP                          dP                    !//
//!  88     88                          88                    !//
//!  88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b.  !//
//!  88     88  88ooood8 88'  '88 88'  '88 88ooood8 88'  '88  !//
//!  88     88  88.  ... 88.  .88 88.  .88 88.  ... 88        !//
//!  dP     dP  '88888P' '88888P8 '88888P8 '88888P' dP        !//
//!===========================================================!//
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return a = std::min(a, b), a == b; }
template <typename T>
bool chmax(T& a, const T& b) { return a = std::max(a, b), a == b; }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
constexpr T popCount(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
constexpr T log2p1(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
constexpr T lsbp1(const T v)
{
#ifdef __has_builtin
    return __builtin_ffsll(v);
#else
    return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); }
//!=====================================================!//
//!  8888ba.88ba             dP            oo           !//
//!  88  '8b  '8b            88                         !//
//!  88   88   88 .d8888b. d8888P 88d888b. dP dP.  .dP  !//
//!  88   88   88 88'  '88   88   88'  '88 88  '8bd8'   !//
//!  88   88   88 88.  .88   88   88       88  .d88b.   !//
//!  dP   dP   dP '88888P8   dP   dP       dP dP'  'dP  !//
//!=====================================================!//
template <typename T>
struct Matrix
{
    Matrix(const std::size_t R, const std::size_t C) : R{R}, C{C}, table(R, std::vector<T>(C, T(0))) {}
    const std::vector<T>& operator[](const std::size_t r) const { return table[r]; }
    std::vector<T>& operator[](const std::size_t r) { return table[r]; }
    Matrix<T> operator-() const
    {
        Matrix<T> ans(R, C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { ans[i][j] = -table[i][j]; }
        }
        return ans;
    }
    Matrix<T> operator+(const Matrix<T>& m) const
    {
        assert(R == m.R);
        assert(C == m.C);
        Matrix<T> ans(R, C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] + m[i][j]; }
        }
        return ans;
    }
    Matrix<T> operator-(const Matrix<T>& m) const
    {
        assert(R == m.R);
        assert(C == m.C);
        Matrix<T> ans(R, C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] - m[i][j]; }
        }
        return ans;
    }
    Matrix<T> operator*(const Matrix<T>& m) const
    {
        assert(C == m.R);
        Matrix<T> ans(R, m.C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < m.C; j++) {
                for (std::size_t k = 0; k < C; k++) { ans[i][j] += table[i][k] * m[k][j]; }
            }
        }
        return ans;
    }
    Matrix<T> operator*(const T& t) const
    {
        Matrix<T> ans(R, C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] * t; }
        }
        return ans;
    }
    template <typename C>
    Matrix<T> operator^(const C n) const { return assert(n > 0), n == 1 ? *this : n % 2 == 1 ? (*this) * ((*this) ^ (n - 1)) : (((*this) * (*this)) ^ (n / 2)); }
    Matrix<T>& operator=(const Matrix<T>& m)
    {
        assert(R == m.R);
        assert(C == m.C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { table[i][j] = m[i][j]; }
        }
        return *this;
    }
    Matrix<T>& operator+=(const Matrix<T>& m)
    {
        assert(R == m.R);
        assert(C == m.C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { table[i][j] += m[i][j]; }
        }
    }
    Matrix<T>& operator-=(const Matrix<T>& m)
    {
        assert(R == m.R);
        assert(C == m.C);
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { table[i][j] -= m[i][j]; }
        }
        return *this;
    }
    Matrix<T>& operator*=(const Matrix<T>& m) { return *this = (*this) * m; }
    Matrix<T>& operator*=(const T& t)
    {
        for (std::size_t i = 0; i < R; i++) {
            for (std::size_t j = 0; j < C; j++) { table[i][j] *= t; }
        }
        return *this;
    }
    template <typename C>
    Matrix<T>& operator^=(const C n) { return (*this) = ((*this) ^ n); }
    const std::size_t R, C;
    std::vector<std::vector<T>> table;
};
template <typename T>
Matrix<T> operator*(const T& t, const Matrix<T>& m) { return m * t; }
template <typename T>
std::ostream& operator<<(std::ostream& os, const Matrix<T>& m)
{
    os << "[\n";
    for (std::size_t i = 0; i < m.R; i++) {
        os << "[";
        for (std::size_t j = 0; j < m.C; j++) { os << m[i][j] << " "; }
        os << "]\n";
    }
    return (os << "]\n");
}
template <typename T>
struct Vector
{
    Vector(const std::size_t R) : R{R}, table(R, T(0)) {}
    const T& operator[](const std::size_t r) const { return table[r]; }
    T& operator[](const std::size_t r) { return table[r]; }
    Vector<T> operator+(const Vector<T>& v) const
    {
        assert(R == v.R);
        Vector<T> ans(R);
        for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] + v[i]; }
        return ans;
    }
    Vector<T> operator-(const Vector<T>& v) const
    {
        assert(R == v.R);
        Vector<T> ans(R);
        for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] - v[i]; }
        return ans;
    }
    Vector<T> operator*(const T& t) const
    {
        Vector<T> ans(R);
        for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] * t; }
        return ans;
    }
    Vector<T>& operator=(const Vector<T>& v)
    {
        assert(R == v.R);
        for (std::size_t i = 0; i < R; i++) { table[i] = v[i]; }
        return *this;
    }
    Vector<T>& operator+=(const Vector<T>& v)
    {
        assert(R == v.R);
        for (std::size_t i = 0; i < R; i++) { table[i] += v[i]; }
        return *this;
    }
    Vector<T>& operator-=(const Vector<T>& v)
    {
        assert(R == v.R);
        for (std::size_t i = 0; i < R; i++) { table[i] -= v[i]; }
        return *this;
    }
    Vector<T>& operator*=(const T& t)
    {
        Vector<T> ans(R);
        for (std::size_t i = 0; i < R; i++) { table[i] *= t; }
        return *this;
    }
    const std::size_t R;
    std::vector<T> table;
};
template <typename T>
Vector<T> operator*(const T& t, const Vector<T>& v) { return v * t; }
template <typename T>
Vector<T> operator*(const Matrix<T>& m, const Vector<T>& v)
{
    assert(m.C == v.R);
    Vector<T> ans(m.R);
    for (std::size_t i = 0; i < m.R; i++) {
        for (std::size_t j = 0; j < m.C; j++) { ans[i] += m[i][j] * v[j]; }
    }
    return ans;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const Vector<T>& v)
{
    os << "[\n";
    for (std::size_t i = 0; i < v.R; i++) { os << v[i] << "\n"; }
    return (os << "]\n");
}
template <typename T>
struct TVector
{
    TVector(const std::size_t C) : C{C}, table(C, T(0)) {}
    const T& operator[](const std::size_t c) const { return table[c]; }
    T& operator[](const std::size_t c) { return table[c]; }
    TVector<T> operator+(const TVector<T>& v) const
    {
        assert(C == v.C);
        TVector<T> ans(C);
        for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] + v[i]; }
        return ans;
    }
    TVector<T> operator-(const TVector<T>& v) const
    {
        assert(C == v.C);
        TVector<T> ans(C);
        for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] - v[i]; }
        return ans;
    }
    TVector<T> operator*(const T& t) const
    {
        TVector<T> ans(C);
        for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] * t; }
        return ans;
    }
    TVector<T>& operator=(const TVector<T>& v)
    {
        assert(C == v.C);
        for (std::size_t i = 0; i < C; i++) { table[i] = v[i]; }
        return *this;
    }
    TVector<T>& operator+=(const TVector<T>& v)
    {
        assert(C == v.C);
        for (std::size_t i = 0; i < C; i++) { table[i] += v[i]; }
        return *this;
    }
    TVector<T>& operator-=(const TVector<T>& v)
    {
        assert(C == v.C);
        for (std::size_t i = 0; i < C; i++) { table[i] -= v[i]; }
        return *this;
    }
    TVector<T>& operator*=(const T& t)
    {
        TVector<T> ans(C);
        for (std::size_t i = 0; i < C; i++) { table[i] *= t; }
        return *this;
    }
    const std::size_t C;
    std::vector<T> table;
};
template <typename T>
TVector<T> operator*(const T& t, const TVector<T>& v) { return v * t; }
template <typename T>
TVector<T> operator*(const TVector<T>& v, const Matrix<T>& m)
{
    assert(v.C == m.R);
    TVector<T> ans(m.C);
    for (std::size_t i = 0; i < m.C; i++) {
        for (std::size_t j = 0; j < m.R; j++) { ans[i] += v[j] * m[j][i]; }
    }
    return ans;
}

template <typename T>
std::ostream& operator<<(std::ostream& os, const TVector<T>& v)
{
    os << "[ ";
    for (std::size_t i = 0; i < v.C; i++) { os << v[i] << " "; }
    return (os << "]\n");
}
//!=========================================!//
//!   888888ba                    dP        !//
//!   88    '8b                   88        !//
//!  a88aaaa8P' .d8888b. 88d888b. 88  .dP   !//
//!   88   '8b. 88'  '88 88'  '88 88888"    !//
//!   88     88 88.  .88 88    88 88  '8b.  !//
//!   dP     dP '88888P8 dP    dP dP   'YP  !//
//!=========================================!//
template <typename T>
std::size_t Rank(Matrix<T> mat)
{
    std::size_t r = 0;
    for (std::size_t c = 0; c < mat.C; c++) {
        if (r == mat.R) { return r; }
        std::size_t piv = r;
        for (; piv < mat.R and mat[piv][c] == 0; piv++) {}
        if (piv == mat.R) { continue; }
        std::swap(mat[piv], mat[r]);
        for (std::size_t j = c + 1; j < mat.C; j++) { mat[r][j] /= mat[r][c]; }
        for (std::size_t j = r + 1; j < mat.R; j++) {
            for (std::size_t k = c + 1; k < mat.C; k++) { mat[j][k] -= mat[r][k] * mat[j][c]; }
        }
        r++;
    }
    return r;
}
//!===============================================================!//
//!   88888888b            dP       .88888.   a88888b. 888888ba   !//
//!   88                   88      d8'   '88 d8'   '88 88    '8b  !//
//!  a88aaaa    dP.  .dP d8888P    88        88        88     88  !//
//!   88         '8bd8'    88      88   YP88 88        88     88  !//
//!   88         .d88b.    88      Y8.   .88 Y8.   .88 88    .8P  !//
//!   88888888P dP'  'dP   dP       '88888'   Y88888P' 8888888P   !//
//!===============================================================!//
template <typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
    if (b == 0) { return std::pair<T, T>{1, 0}; }
    const auto p = extgcd(b, a % b);
    return {p.second, p.first - p.second * (a / b)};
}
template <typename T>
constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; }
//!========================================================!//
//!  8888ba.88ba                 dP    dP            dP    !//
//!  88  '8b  '8b                88    88            88    !//
//!  88   88   88 .d8888b. .d888b88    88 88d888b. d8888P  !//
//!  88   88   88 88'  '88 88'  '88    88 88'  '88   88    !//
//!  88   88   88 88.  .88 88.  .88    88 88    88   88    !//
//!  dP   dP   dP '88888P' '88888P8    dP dP    dP   dP    !//
//!========================================================!//
template <uint mod>
class ModInt
{
private:
    uint v;
    static uint norm(const uint& x) { return x < mod ? x : x - mod; }
    static ModInt make(const uint& x)
    {
        ModInt m;
        return m.v = x, m;
    }
    static ModInt power(ModInt x, ll n)
    {
        ModInt ans = 1;
        for (; n; n >>= 1, x *= x) {
            if (n & 1) { ans *= x; }
        }
        return ans;
    }
    static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; }

public:
    ModInt() : v{0} {}
    ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {}
    ModInt(const ModInt<mod>& n) : v{n()} {}
    explicit operator bool() const { return v != 0; }
    ModInt<mod>& operator=(const ModInt<mod>& n) { return v = n(), (*this); }
    ModInt<mod>& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); }
    ModInt<mod> operator+() const { return *this; }
    ModInt<mod> operator-() const { return make(norm(mod - v)); }
    ModInt<mod> operator+(const ModInt<mod>& val) const { return make(norm(v + val())); }
    ModInt<mod> operator-(const ModInt<mod>& val) const { return make(norm(v + mod - val())); }
    ModInt<mod> operator*(const ModInt<mod>& val) const { return make((uint)((ll)v * val() % (ll)mod)); }
    ModInt<mod> operator/(const ModInt<mod>& val) const { return *this * inv(val()); }
    ModInt<mod>& operator+=(const ModInt<mod>& val) { return *this = *this + val; }
    ModInt<mod>& operator-=(const ModInt<mod>& val) { return *this = *this - val; }
    ModInt<mod>& operator*=(const ModInt<mod>& val) { return *this = *this * val; }
    ModInt<mod>& operator/=(const ModInt<mod>& val) { return *this = *this / val; }
    ModInt<mod> operator+(const ll val) const { return ModInt{v + val}; }
    ModInt<mod> operator-(const ll val) const { return ModInt{v - val}; }
    ModInt<mod> operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; }
    ModInt<mod> operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; }
    template <typename I>
    ModInt<mod> operator^(const I n) const { return power(v, n); }
    ModInt<mod>& operator+=(const ll val) { return *this = *this + val; }
    ModInt<mod>& operator-=(const ll val) { return *this = *this - val; }
    ModInt<mod>& operator*=(const ll val) { return *this = *this * val; }
    ModInt<mod>& operator/=(const ll val) { return *this = *this / val; }
    template <typename I>
    ModInt<mod>& operator^=(const I n) { return (*this) = ((*this) ^ n); }
    bool operator==(const ModInt<mod>& val) const { return v == val.v; }
    bool operator!=(const ModInt<mod>& val) const { return not(*this == val); }
    bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); }
    bool operator!=(const ll val) const { return not(*this == val); }
    uint operator()() const { return v; }
};
template <uint mod>
inline ModInt<mod> operator+(const ll val, const ModInt<mod>& n) { return n + val; }
template <uint mod>
inline ModInt<mod> operator-(const ll val, const ModInt<mod>& n) { return ModInt<mod>{val - (ll)n()}; }
template <uint mod>
inline ModInt<mod> operator*(const ll val, const ModInt<mod>& n) { return n * val; }
template <uint mod>
inline ModInt<mod> operator/(const ll val, const ModInt<mod>& n) { return ModInt<mod>(val) / n; }
template <uint mod>
inline bool operator==(const ll val, const ModInt<mod>& n) { return n == val; }
template <uint mod>
inline bool operator!=(const ll val, const ModInt<mod>& n) { return not(val == n); }
template <uint mod>
inline std::istream& operator>>(std::istream& is, ModInt<mod>& n)
{
    uint v;
    return is >> v, n = v, is;
}
template <uint mod>
std::ostream& operator<<(std::ostream& os, const ModInt<mod>& n) { return (os << n()); }
//!============================================!//
//!    8888ba.88ba             oo              !//
//!    88  '8b  '8b                            !//
//!    88   88   88  .d8888b.  dP  88d888b.    !//
//!    88   88   88  88'  '88  88  88'  '88    !//
//!    88   88   88  88.  .88  88  88    88    !//
//!    dP   dP   dP  '88888P8  dP  dP    dP    !//
//!============================================!//
int main()
{
    using Mat = Matrix<ModInt<2>>;
    int N, M, X;
    std::cin >> N >> M >> X;
    Mat mat(M + 30, N + 1);
    for (int j = 0; j < N; j++) {
        int A;
        std::cin >> A;
        for (int i = 0; i < 30; i++) { mat[i][j] = (A & (1 << i)) != 0; }
    }
    std::vector<int> T(M);
    for (int i = 30; i < M + 30; i++) {
        int l, r;
        std::cin >> T[i - 30] >> l >> r;
        for (int j = l - 1; j < r; j++) { mat[i][j] = 1; }
    }
    const int rank1 = Rank(mat);
    for (int i = 0; i < 30; i++) { mat[i][N] = (X & (1 << i)) != 0; }
    for (int i = 30; i < M + 30; i++) { mat[i][N] = T[i - 30]; }
    const int rank2 = Rank(mat);
    if (rank1 != rank2) { return std::cout << 0 << std::endl, 0; }
    ModInt<MOD> ans = 1;
    for (int i = 0; i < N - rank1; i++) { ans *= 2; }
    std::cout << ans << std::endl;
    return 0;
}
yukicoder

結果

テストケース

ソースコード
